Posts Tagged: Math

In the Classroom Professional Learning
Less Work (Teacher) + More Work (Student) = Rigor
June 10, 2017
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Less Work (Teacher) + More Work (Student) = Rigor

Cindy Cliche

As another school year comes to a close, many educators reflect on successes and begin to set goals for the upcoming year. One word seems to be a part of many conversations: RIGOR. It comes up in evaluation conferences, Professional Learning Communities (PLC), and grade level planning team meetings. Yet many educators still seem to have some confusion about what rigor looks like in the classroom.
In the Classroom Professional Learning
Blended Learning and Education
June 3, 2017
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Blended Learning and Education

Elaine Vaughan

Blended Learning: When I first heard those words, I was not impressed. I imagined all my students doing their math on a computer with little or no assistance from me. I knew that within 3 years my students would each have a laptop so I started doing some research on integrating mathematics and technology. I learned very quickly that my interpretation of blended learning would take on a new role and realized that I could combine classroom learning with online learning in which my students could, in part, control the time, pace, and place of their educational experiences. I also discovered two main ideas concerning differentiation and the mathematical practices and how my support of a blended learning environment within the classroom could enhance student learning.

Differentiation and Blended Learning: Every educator’s desire is to determine the learning styles (visual, kinesthetic, or auditory) of the students in the classroom and promote student investigation through multiple representations. Students may discover and experiment with graphing, examining tables, and analyzing concepts by using free online tools such as Desmos and Geogebra. A teacher should carefully evaluate the technological resources to assure the support of student learning of mathematics and the advantages offered in posing mathematical problems as well as illustrating mathematical ideas.

The Mathematical Practices and Blended Learning: Many of the Mathematical Practices dealing with problem solving, reasoning and constructing viable arguments, modeling with mathematics, and using appropriate tools are supported by various online programs and videos. Dan Meyer has developed many mathematical exercises that not only incorporate the practices into learning but also create scenarios that prompt students to stop and think about how to formulate solutions to the problems. One of these problems is called Meatballs and the Three Act Math Task: Will It Overflow? ( Students work with the information observed in the three videos to solve the problem.  Educators may also choose Khan Academy, create flipped lessons, or use lessons from YouTube for students who need more practice or understanding on standards. Teachers also have various alternatives for on-line formative assessment such as Kahoot, Google Forms, Socrative, Quizlet, or student designed presentation using Screencast-O-Matic. Listed are just a few of the online learning tools for educators to use in the classroom.

Three years have passed since I first heard about Blended Learning. The ninth and tenth graders at my high school all have laptops for learning. I now realize that I will never be replaced by a computer and that I may serve as a facilitator in the classroom. The questioning techniques along with problem solving progress at a much higher level of learning for students. I am also preparing my students for the future world of work through the collaborative and communication skills they are utilizing with their peers. As an educator, one needs to keep in mind that all of the learning tools available for students take time to implement or adapt for multiple learning styles and that the technology should always support the mathematics. Also, an educator may want to investigate online professional development (MOOC-Ed, North Carolina State, Whatever the decisions made in moving students forward in a technological world, the rewards far outweigh the drawbacks. I am now convinced that a Blended Learning environment will enhance my students’ work skills as they become productive citizens of the future.

Dr. Elaine Vaughan is a mathematics instructor at Oak Ridge High School for 20 years. She is a National Board Certified teacher, Professional Learning Communities Coach, and member of the Response to Intervention district and school board. Elaine is also a member of Delta Kappa Gamma and serves on the XI State Vision Board. Through this organization, she received both state and international scholarships. Elaine was a state mathematics textbook reviewer during the 2013-2014 school year. Elaine received her Bachelor’s and Master’s degree in Mathematics Education from the University of Tennessee and her doctorate from Walden University. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.

In the Classroom
Math Homework 101 for Parents
February 18, 2017
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Math Homework 101 for Parents

Cindy Cliche

It is a cold winter night and seated at the kitchen table are a little girl and her dad struggling with math homework.  Dad is showing his daughter how to solve the problem and his child is crying because he is not solving it the way the teacher showed the class.   This scenario happened over 50 years ago as my dad tried to help me with math homework.  As an educator I still get the question from parents, “How do I help my child with math homework?  They do it differently than when I was a child.”

Thinking about this question, I offer the following tips:

  1. Keep a positive attitude.  (Fake it until you make it!)  
    As adults we are the role models for our children.  Think about the messages you are sending to your child.  They not only hear what you say but also read your body language and the tone of your voice.  Keep this in mind.  It is okay to say this problem is difficult. Parents can get confused too,  but we will work hard to solve it. Then celebrate with your child when you finally have the solution.  This mathematical struggle is actually a good thing-it means your child’s brain is growing!  There is no better feeling when you accomplish a difficult task.
  2. Math = Discussion
    Solve a problem independently and then share the way you thought about the problem.  Listen to the way your child solved the problem.  Discuss how the way you solved is the same and/or different.  I have found that listening to the students’ thinking has helped me see the problem differently and deepened my understanding of the mathematics.
  3. Allow mistakes.
    Let your child struggle with the math, because it can lead to a deeper understanding of the concept.   Allow and even encourage them to persevere through different ways to solve the problem.  You might even pose questions such as:  Could you draw a model/diagram to help you?  What is the question you need to answer?  Support learning through questioning.
  4. Provide a math toolbox.
    Encourage your child to use tools to solve a problem.  It is important to provide “tools before rules.” Here is a sample of some tools that can be collected and put in a container:
    Grid paper
    Hundreds Chart
    Tens Frame and/or Double Tens Frame
    Counters such as buttons, pennies, paper clips, dried beans. Keep these tools in a convenient location so they are available during homework.
  5. Make math fun and engaging daily.
  • View the world through a mathematical lens. Involve your child in cooking and be sure to notice the fractions as you are making that special recipe.
  • Allow your child opportunities to count money.  You can skip-count nickels or dimes.  Ask your child to count coins when paying at the store or making change.
  • Ask your child the time on analog and digital clocks.  Ask how much time will pass before we leave for soccer practice.  Soccer practice is one hour; what time will it end?  Allow them the opportunity to plan a schedule for a day of vacation.
  • Look for the math in real-world situations.  Take pictures of the math you see in the world around you.  Ask the questions:  What do you notice?  What do you wonder?

    This was a picture sent to me by one of my students.  The child noticed this in the grocery and began wondering how many cans were in the display.  The mom gave him time to explore and he sent me the picture with the answer of how many cans.  Allow these opportunities for your child.  Math is everywhere!

Some of my special memories are times I spent with my dad as he shared his passion for mathematics.  The ideas shared in this article were inspired by him as he helped me truly see the world through a mathematical lens.   Be that inspiration for your child and you will ignite a lifelong passion in your child.

Cindy Cliche has over 30 years of classroom experience and currently serves as the Math Coordinator for Murfreesboro City Schools. She also teaches Math Methods to pre­-service teachers at Middle Tennessee State University. Cindy has worked in the past as a Teacher Trainer with the Tennessee State Department of Education. She was the Presidential Awardee in Math and Science Teaching in 2004. She has a passion for math education in the elementary grades. Cindy received her Bachelor’s Degree from Ball State University and her Masters from Berry College. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.

In the Classroom Professional Learning
One-to-One with Technology: What Does it Look Like?
December 20, 2016
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One-to-One with Technology: What Does it Look Like?

Jessica Childers

To be ready for the jobs of the future, students must learn to use technology. David Warlick, an influential educator and author, wrote, “We need technology in every classroom and in every student and teacher’s hand, because it is the pen and paper of our time, and it is the lens through which we experience much of our world.” For the past three years, our school has worked to become one-to-one with students and technology.

This year, at our school, every classroom has a full set of Chromebooks or Macbooks. Students have a Gmail account with access to the G-Suites programs. They are able to understand, apply, analyze, evaluate, and create using the technology in the classroom. Teachers have created lessons, posted them on Google Classroom, and assessed student learning using this technology as well. However, this looks different in every classroom, and most teachers have found what works best for them. I have heard from some teachers at other schools that they have been given a cart of Chromebooks with no training. Often they are afraid to dive in and try new things with students, fearing failure. Here’s what technology use looks like in our 5-8 middle school:

In an English/Language Arts classroom, the teacher has posted a PDF file on Google Classroom. The students open the file using the Chrome add-on Kami which allows them to annotate directly on the document. Before, the teacher would have needed to make 100 copies and ensure each student has the right colors of highlighters. In another classroom students are practicing for a vocabulary test that is coming up on Friday by using Quizlet, Quizlet Live, Flocabulary, Kahoot, and Quizizz. With these programs, the students can receive immediate feedback about their answers and the teacher can formatively assess their learning. Also, most of the students enjoy these programs because they are set up like games and competitions.

In a Science and Social Studies classroom students are creating one presentation using Google Slides about animal adaptations and another about important battles from the Civil War. They are collaborating with their partners by sharing the slides through Google Drive and giving feedback to each other to improve the finished product. Students research their topics using the internet and add images and videos to their slides. When finished, the students present their slideshows to the class. The teacher uses a rubric to evaluate their slides, presentations, and group work. Once all the presentations are complete, the class is quizzed about highlights from the slideshows.

In a Math classroom, the teacher has posted four videos to Google Classroom. These videos are created by Khan Academy and linked through YouTube. Students are given one week to watch all four videos, which lets them see the lesson presented another way. Once they have watched the videos, students must complete three assignments on Each time a student enters an answer on IXL, they get immediate feedback about the response and are given the correct path to solve it if the answer was wrong. Students must write down the problems from IXL, show work and answers, and turn in their papers to the teacher by Friday. The teacher still uses direct instruction, group work, and discussion to teach. However, much of the practice is moved from worksheets to online programs that assess the same skills.

All teachers still have the autonomy to teach their classes the way they see fit. Most teachers still use direct instruction daily with students. What has changed most for our school is the work that students are producing. Instead of making a poster, students can create a slideshow; instead of hand writing an essay, students can type one; and instead of doing a worksheet, students can practice online. As our school becomes more comfortable with the technology, the teaching and learning will only continue to improve and help students learn skills necessary for their future.

Jessica has taught middle school math in Putnam County Schools for the past 7 years. She first worked at Avery Trace Middle School teaching 6th, 7th and 8th grade math. Then she moved to Cornerstone Middle School, which is now Upperman Middle School, to teach 5th grade math. During this time, she has served as the 5th grade team leader, mentor teacher, 2015 school level Teacher of the Year, digital transition team member and mathematics instructional specialist. She holds a Bachelor’s degree in Multidisciplinary Studies – Middle School and a Master’s degree in Curriculum and Instruction, both from Tennessee Tech University. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.

In the Classroom Leadership
Music Teacher to Reading Interventionist: Helping your non reading/math teachers fill your need for RTI interventionists
December 19, 2016
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Music Teacher to Reading Interventionist: Helping your non reading/math teachers fill your need for RTI interventionists

Crystal Nelson

RTI2 (Response to Intervention and Instruction) is no longer a new concept for many schools, but some are still trying to figure it out.  Finding the personnel to teach reading and math intervention groups has led many administrators to pulling in non-reading/math teachers to lead these interventions.  I was asked, as a music teacher, to take on a first grade tier 3 reading intervention group.  Based on my experiences, I have compiled some suggestions for administrators to support teachers who are asked to step way out of their comfort zones to teach something they have never taught before.
  1. Understand teachers might be dealing with some cognitive dissonance. Even when the  teacher wants to be flexible to do what’s best for the students and the school, it’s difficult not to question, “Is it reasonable to ask me to teach math or reading (already the subjects that get all the attention and emphasis) when I’m a music teacher (aka teacher of a subject that is already way undervalued in education and possibly in your school)?”  The positive attitude is the teacher’s responsibility, but you still need to be aware these are very real feelings grounded from a very real place. Furthermore, it is probably a reality that the non-tested subjects in your school have probably had their time cut or have students pulled out, or both.  When I first started, I was getting my Master’s in Educational Leadership, so my perspective had shifted with that program of study to where I was able to approach taking a reading intervention group differently than I would have two years earlier. Mentally, I was already there, so my principal did not have to make the case with me. For administrators with teachers who aren’t coming from this same place, I would suggest creating a need for those changes. Pose the problem in a context that allows the teacher to see the larger picture and how these changes are necessary to student success.
  2. Provide helpful training. Effective training can reinforce the benefits of a structured program teachers are using during intervention time and help fill in gaps in knowledge. If a structured program is not available, good training is imperative. Luckily, the state of Tennessee was providing some Intervention and Common Core trainings the summer after I started RTI interventions. These trainings detailed the components of learning to read (decoding, fluency, comprehension, etc.) and intervention strategies for those components.  Your state’s department of education might have resources or materials available to help train your teachers.
  3. Create a safe environment. Remember, these teachers are possibly feeling really insecure about their ability to teach something new and might be a little terrified they’re going to permanently damage the children. (Rationally, they know this isn’t likely, but it’s still a fear!) Your teachers need to feel safe enough to ask questions about what they are doing and to be able to address concerns. It’s a good idea to provide some extra supervision or informal observations in the beginning. My first year, I started out at a table in a strong teacher’s room with my intervention group, and she had another group at another table. She was able to monitor some to know I was on-track, and it made me feel a lot better. Later in the year, I moved into a quieter area, but my assistant principal was still in every so often to do fidelity checks. I had no qualms saying, “Let me know if I need to do something differently.” In a way, it’s easier to ask for help when you aren’t supposed to be the expert. I would be less eager to show my vulnerability in the music classroom. Last year, I had a math group for the first time, no structured program— just me trying to figure out what the students needed and trying to figure out the most logical way to structure the content. I was somewhat uncomfortable with my assistant principal in there watching, but I said, “Feel free to jump in if you see something that I should do differently.” I recognize doing right by the students trumps my discomfort at someone else observing me do something poorly. As it turns out, she was happy with the work I was doing. Being able to discuss why I chose the focus I did and having discussions about how I’m teaching, helped me feel a lot more secure.
  4. If at all possible, have your teachers use a structured program. This provides the appropriate sequencing and activities needed to teach the given skill. Using a structured program gave me a solid foundation of knowledge and gave me a sense of security knowing I wasn’t going to do anything horribly wrong. As confidence builds, it doesn’t take long before teachers can use their best judgement and make modifications as needed.
  5. Encourage teachers to make connections between teaching their subject and teaching a totally new subject. I have discovered that teaching reading is incredibly similar to teaching music. There are content-specific things I need to know and have learned, but the “how” of teaching decoding, building fluency, analyzing, and teaching from literature is shockingly similar. Even when it came to math, I just used my knowledge of how to break down the goal, “what I want the children to be able to do,” and take it back until I’ve figured out the steps needed to meet that goal.

Obviously, how you approach your non-reading/math teachers with leading intervention groups will have to do with the individual personalities of those teachers, as well as the resources you have available. You might have a situation where the teacher can observe other groups, you might need to set up clear expectations for how intervention time should look, etc.  But I wanted to share what made me successful as an interventionist.  Basically, provide teachers with the resources they need to be successful (materials, training) and treat them with the same understanding you would need if you were in the same situation.

Crystal has taught at Camden Elementary for six years teaching PreK-2nd grade general music and reading intervention and serves as RTI Co- Coordinator. Crystal served as the Benton County Education Association president 2013-2015, is an active member of Delta Kappa Gamma, and was named Distinguished Educator of West Tennessee by the Tennessee Education Association in 2014. Crystal is a graduate of the University of Tennessee at Martin where she earned a B.M. in Music Education. As a life-learner, she has also earned her Master’s degree in Educational Leadership and an Ed.D. in Leadership and Professional Practice from Trevecca Nazarene University. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.

In the Classroom
RTI2 Math: Inspiration Plus Intervention Equals Improvement
July 15, 2016
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RTI2 Math: Inspiration Plus Intervention Equals Improvement

Maureen Henderson

Anine-year-old child steps up to the plate on a cool spring night. The clamor of the audience is immediate and fierce. You can do it! You’ve got this!

The first pitch is thrown. Strike one! The audience response is full of echoes of encouragement. It’s okay! Come on! Next pitch, the child swings hard and gets a hit, but it goes foul. Strike two! The crowd starts yelling more loudly now. Good try! You’re a hitter! You’re gonna get this one! The third pitch whizzes into the catcher’s glove. Strike three! The child walks toward the dugout, head down, feeling defeated.

What strategies might the coach of this young boy use next to help his player persevere? Most likely he would start by offering words of encouragement as a source of motivation and inspiration to the child. Additionally, he would provide intervention focused on batting strategies in the practice sessions that follow. Before the next game, the coach would spend much time reinforcing skills that would build this child’s confidence, and as a result of the inspiration and intervention provided, the player would soon show improvement on the field.

My mind immediately begins to wander and quickly transforms from baseball mom to fourth grade classroom teacher. I wonder if that is how the kids in my Response to Instruction and Intervention (RTI2) math group feel? First grade—adding and subtracting. Strike one! Second grade—time and money. Strike two! Third grade—multiplication facts. Strike three… you’re out! Now here they are approaching the plate in fourth grade ready to take another swing at learning.

Thinking of the RTI2 program as our playing field, I reflect on the Hope Street Group Tennessee Teacher Fellow’s Spring 2016 Report that suggests four key areas to consider in supporting successful RTI2 implementation to ensure that every child is a winner:

  • necessary tools that allow for effective scheduling and structure of the RTI2 program
  • more support to promote positive school climates that embrace RTI2 as beneficial
  • a specific RTI2 contact person within each district to improve communication between parents, schools, and the state
  • additional resources, professional development, and increased staffing to assist teachers with their daily RTI2 instruction.   

As an RTI2 teacher, I believe that if we fully execute the above four key areas, then students ready to take a swing at fourth grade math will have many amazing opportunities. They can secure a base hit by receiving intervention while their Tier I instruction is protected. They could get all the way to second by having a positive, cohesive school-wide team. They may even hit a triple because all stakeholders involved believe in their ability to grow and learn. All of these children can have a chance at a home run in a school with great resources and well-trained teachers.

Implementing an RTI2 program which includes the recommendations stated in the Hope Street Group Report will give all children the inspiration plus the intervention needed to equal improvement. They will have everything they need to hit a grand slam!

Maureen Henderson teaches fourth grade math, science, and social studies at Greenbrier Elementary School in Robertson County. She has been an educator in Robertson County for seventeen years. Maureen has served as a grade level leader and as a chair for the school’s math committee. She also serves as a Hope Street Group Tennessee Teacher Fellow, engaging her colleagues in providing classroom feedback to the Tennessee Department of Education on public education policy issues.